Francis wheel and hydraulic machine comprising one such wheel

ABSTRACT

A Francis runner that includes a crown, a band and blades which extend between the crown and the band. An angle (β 24 ) between a linear speed (U, D 224 ) of one of the blades and a median of the blade at the trailing edge, has a value between 20 and 25°. As a result, a machine utilizing the Francis runner of the invention is efficient, while an equivalent power under high load is high.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a Francis runner and to a hydraulic machineequipped with such a runner.

Francis runners can equip different sorts of hydraulic machines, such asturbines, pumps, or pump-turbines. They comprise blades distributedabout a central rotating shaft and define therebetween channels for flowof water. The geometry of the blades of these runners is defined so thatthe flow of the water induces a torque on the runner, in the case of aturbine, or so to transmit a movement to the fluid, in the case of apump. The power that a hydraulic machine equipped with such a runner candeliver depends on its geometry and on the type of heads with which itis associated. In this way, the power that a turbine can deliver may bebrought to a reference value defined by the equivalent power deliveredby a turbine of the same geometry working under 1 metre of head andwhose runner outlet diameter is 1 metre. This power P₁₁ depends inparticular on the speed of rotation N₁₁ of the turbine under the sameconditions.

2. Description of the Related Art

As is visible in FIG. 6, an optimal working point A may be defined in asystem of coordinates giving the power P₁₁ of a turbine, under theaforementioned conditions, as a function of the speed of rotation N₁₁under the same conditions. There is defined as power under high loadP_(11FC), the power of the turbine for an efficiency less by 3.5% thanthe efficiency at point A. In the reference system P₁₁ on N₁₁, curvesI₉₉, I₉₈, I₉₇, etc. of constant values of the efficiency obtained with aturbine are defined. Furthermore, there is defined a noteworthy point Bof the same abscissa as point A and for which the power obtained isequal to P_(11FC).

There is defined as equivalent power under high load P_(11FC), the powerobtained under the conditions of point B for each turbine.

As shown in FIG. 7, present-day turbines have equivalent powers underhigh loads P_(11FC) which, in a representation as a function of thespeed N₁₁ mentioned hereinabove, lie in a first zone Z₁, which showsthat the equivalent power under high load P_(11FC) increases as afunction of the speed N₁₁. It is sometimes necessary to obtainrelatively high equivalent powers under high loads. In particular, inthe case of rehabilitation of an existing installation, the speed N₁₁ isimposed, this in practice limiting the power values P_(11FC) that may beobtained with a conventional turbine.

Up to the present time, equivalent power zones under high loads ofrelatively high values with respect to the speed N₁₁ have not beenreally explored by the designers of hydraulic machines, as solutionsdegraded from the technical/economical standpoint were expected.

SUMMARY OF THE INVENTION

The present invention takes the opposite view to this prejudice of theperson skilled in the art by exploring the ranges of values offlowrates, of powers and of speeds of the hydraulic machinescorresponding approximately to zone Z₂ in FIG. 7. It has proved that ajudicious choice of certain characteristics of the turbine runner makesit possible to obtain solutions offering a better level of efficiency,as will appear from the following explanations.

In this spirit, the invention relates to a Francis runner whichcomprises a crown, a band and blades extending between this crown andthis band, these blades-defining between themselves channels for flow ofliquid. This runner is characterized in that the angle between thelinear speed of progress of one of the blades and the median line ofthat blade at the level of its trailing edge, has, in the vicinity ofthe point of attachment of the blade on the band, a value includedbetween 20 and 25°.

Thanks to the invention, the orientation of the trailing edge of theblades with respect to their linear direction of progress issufficiently important for a considerable flowrate of liquid to be ableto transit via the runner, this making it possible to attain powervalues notably higher than those known in the machines of the state ofthe art, without degrading the efficiency of the machine.

According to advantageous but non-obligatory aspects of the invention,this runner incorporates one or more of the following characteristics:

-   -   Over the length of the trailing edge of the blade, the angle        between the linear speed and the aforementioned median line has        a maximum value less than 34°.    -   Over the length of the trailing edge of the blade, the angle        between the linear speed and the aforementioned median line has        an average value included between 20 and 30°.    -   Over the length of the leading edge of the blade, the mean angle        between the linear speed and the median line of this blade at        the level of the leading edge has a value included between 70        and 120°.    -   The angle between the linear speed and the aforementioned median        line has, in the vicinity of the point of attachment of the        blade on the band, a value included between 70 and 120°.    -   The overlap angle between the leading edge and the trailing edge        of the blade has, viewed in a direction parallel to the axis of        rotation of the runner:

-   at the level of the band, a value less than 25°.

-   at the level of the crown, a value less than 37° and

-   on average, over the length of the leading and trailing edges, a    value less than 31°.    -   The band has a meridian section such that its minimum diameter        over the central third of its height is less by at least 2% with        respect to the diameter of the band at the level of the points        of attachment of the trailing edges of the aforementioned        blades.

The invention also relates to a hydraulic machine of Francis type whichcomprises a runner as described previously. Such a machine may beconstituted by a turbine adapted to deliver an equivalent power underhigh loads, under 1 metre of head and with a runner outlet diameter of 1metre, expressed in kilowatts, such that its ratio with the speed ofrotation of the turbine under the same conditions, expressed in rpm, hasa value included between 0.16 and 0.175. Surprizingly, such a machinehas a satisfactory efficiency, in the ranges of N₁₁ usually used.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more readily understood and other advantagesthereof will appear more clearly in the light of the followingdescription of a form of embodiment of a Francis turbine according tothe invention, given solely by way of example and made with reference tothe accompanying drawings, in which:

FIG. 1 is a view in perspective of a Francis turbine runner according tothe invention.

FIG. 2 is a meridian half-section of the runner of FIG. 1.

FIG. 3 is a developed section of the profile of the blade shown in FIG.2 along line III.

FIG. 4 is a section similar to FIG. 3 in the zone of join between theblade and the band, along line IV in FIG. 2.

FIG. 5 is a plan view from above of the blade shown in FIGS. 2 to 4, thecrown and the band having been omitted to render the drawings clearer.

FIG. 6 schematically shows the curves of constant efficiency as afunction of the equivalent power of a turbine and of the speed ofrotation under the conditions mentioned hereinabove, and

FIG. 7 is a schematic representation of the distribution of theequivalent powers under high load (P_(11FC)) of different turbines as afunction of their speeds of rotation under the aforementionedconditions.

DESCRIPTION OF THE EMBODIMENT

The runner 1 shown in FIGS. 1 to 5 comprises identical blades 2distributed about a central axis X–X′ of rotation of the runner 1. Acrown 3 is provided in the upper and internal radial part of the runner1, while a band 4 borders the lower, radial and external part of theblades 2. A flow channel 5 is thus defined between each pair of twoadjacent blades, this channel being bordered by the crown 3 and the band4.

The blade 2 includes a leading edge 21 and a trailing edge 22. Ajunction 213 is formed between the edge 21 and the crown 3. Anotherjunction 214 is formed between the edge 21 and the band 4. A furtherpoint of junction 223 is formed between the edge 22 and the crown 3 andanother point of junction 224 is formed between the edge 22 and the band4.

The line III in FIG. 2 represents the meridian trace of a sheet ofaxisymmetrical flow along the blade 2. Arrows E represent this flow.

In the representation of FIG. 3, the flow E is globally perpendicular tothe direction of the speed U of linear progress of the blade 2 whosevalue is equal to the number of revs per minute made by the runner 1multiplied by π and by the nominal diameter of the runner.

A surface of junction 23 is formed between the blade 2 and the crown 3,this surface including points 213 and 223. Furthermore, 24 denotes thesurface of junction between the blade 2 and the band 4, this surfaceincluding points 214 and 224. An imaginary curved surface correspondingto the median line of the blade 2 is shown at 25, i.e. to a surfacelocated at equi-distance from the lateral faces 26 and 27 of the blade2. The trace of the surface 25 in the plane of FIG. 3 is a curveequi-distant from the lateral faces 26 and 27.

Δ₁ denotes a straight line passing through the leading edge 21 andextending the median line 25 in the plane of FIG. 3. β₁ denotes theangle between this straight line Δ₁ and a straight line D₁ parallel tothe speed U and passing through the leading edge 21.

In the same way, Δ₂ denotes a straight line extending the median line 25at the level of the trailing edge 22 of the blade 2 and D₂ a straightline parallel to the speed U at the level of this trailing edge. β₂denotes the angle between the straight lines Δ₂ and D₂.

It will be understood that, taking into account the essentiallynon-planar nature of the blades 2, the values of the angles β₁ and β₂are variable over the length of the leading edge 21 and trailing edge22.

As is more particularly visible in FIG. 4, the value of the angle β₂₄corresponding to the angle β₂ at the level of point 224, is includedbetween 20 and 25°, in practice equal to 21° in the example shown. Theangle β₂₄ is the angle between a straight line Δ₂₂₄ extending the medianline 25 to point 224 and a straight line D₂₂₄ parallel to the speed Uand passing through that point.

An angle β₁₄, corresponding to angle β₁ at the level of point 214, isdefined between a straight line D₂₁₄ parallel to speed U and passingthrough that point and a straight line Δ₂₁₄ extending the median line 25on that point. The value of this angle β₁₄ is included between 70 and120° and, preferably, of the order of 85° as shown in FIG. 4.

In practice, each blade 2 is designed and made so that the maximum valueof the angle β₂, over the length of the trailing edge 22, is less than34°. A mean value of this angle β₂ may also be defined, taken overtwenty five streams of flow equally distributed between the crown 3 andthe band 4. This mean value is preferably included between 20 and 30°.

Thanks to these values of the angle β₂, the flow at the level of thetrailing edge 22 may take place with a relatively high flowrate, withoutreduction of the efficiency of the runner 1.

Similarly, the mean value of the angle β₁ over the length of the leadingedge 21, taken under the same conditions, is included between 70 and120°.

Referring to FIG. 5, the overlap angle φ₂₄ of the blade 2 at the levelof the band 4 may also be defined as being the angle between a planeP₂₂₄ passing through axis X−X′ and through point 224 and a plane P₂₁₄passing through axis X–X′ and through point 214.

In the same way, the overlap angle φ₂₃ of the blade 2 at the level ofthe crown 3 is defined as being the angle between a plane P₂₂₃ passingthrough axis X–X′ and through point 223 and a plane P₂₁₃ passing throughaxis X–X′ and through point 213.

In order to optimize the flow of the water in the channels 5, the valueof φ₂₄ is chosen to be less than 25°, while the value of φ₂₃ is chosento be less than 37°. In addition, a mean value of the angle of overlapbetween the leading and trailing edges of the blade 2 over the length ofthese edges may be defined by forming the average of 25 values of anglesφ between planes P₂₂ passing through the axis X–X′ and successive pointsdistributed equally over the trailing edge 22 and planes P₂₁ passingthrough axis X–X′ and successive points distributed equally over theleading edge 21. In practice, the mean value φ_(m) of this angle ischosen to be less than 31°.

As is more particularly visible in FIG. 2, the band 4 may be dividedinto three bands 42, 43 and 44 whose unitary height h₄₂, h₄₃ and h₄₄ isequal to one third of the total height h₄ of the band 4. Considering theintermediate band 43 of the band 3, its minimum internal diameterD_(min) can be defined, which is in fact the minimum diameter of thesurface 41. The diameter D₂₂₄ of the surface 41 at the level of point224 can also be defined.

In practice, the ratio of D_(min)/D₂₂₄ is less than 0.98, whichcorresponds to the fact that the minimum diameter is smaller by at least2% than the diameter D₂₂₄.

1. A Francis runner comprising: a crown; a band; and blades extendingbetween said crown and said band such that a leading edge of each ofsaid blades has points of attachment with said crown and said band and atrailing edge of each of said blades has other points of attachment withsaid crown and said band, said blades defining between themselveschannels for flow of liquid and being rotatable with said crown and saidband in a direction defined by a linear component (U), and each of saidblades has oppositely oriented lateral faces which are spacedequidistant from an imaginary curved median line extending from saidleading edge to said trailing edge; wherein an angle (β₂₄) between thedirection defined by the linear component (U) of each of said blades anda straight line (Δ₂₂₄) extending from the median line of each of saidblades at said trailing edge thereof, has, at said point of attachmentof each of said blades on said band, a value between 20 and 25°.
 2. Therunner according to claim 1, wherein, over a length of said trailingedge of each of said blades, an angle (β₂) between said directiondefined by the linear component (U) and a straight line (Δ₂) extendingfrom the median line of each of said blades at said trailing edgethereof has a maximum value less than 34°.
 3. The runner according toclaim 1, wherein, over a length of the trailing edge each of saidblades, an angle (β₂) between said direction defined by the linearcomponent (U) and a straight line (Δ₂) extending from the median line ofeach of said blades at said trailing edge thereof has an average valuebetween 20 and 30°.
 4. The runner according to claim 1, wherein, over alength of the leading edge of each of said blades, an angle (β₁) betweensaid direction defined by the linear component (U) and a straight line(Δ₁) extending from the median line of each of said blades at saidleading edge thereof has a value between 70 and 120°.
 5. The runneraccording to claim 1, wherein an angle (β₁₄) between said directiondefined by the linear component (U) and a straight line (Δ₂₁₄) extendingfrom the median line of each of said blades at said leading edge thereofhas, in the vicinity of said point of attachment of each of said bladeson said band, a value between 70 and 120°.
 6. The runner according toclaim 1, wherein an overlap angle between said leading edge and saidtrailing edge of each of said blades has, viewed in a direction parallelto an axis of rotation (X–X′) of the runner: at said band, a value (φ₂₄)less than 25°; at said crown, a value (φ₂₃) less than 37°; and onaverage, over lengths of said leading and trailing edges, a value(φ_(m)) less than 31°.
 7. The runner according to claim 1, wherein saidband has a meridian section such that a minimum diameter (D_(min)) ofsaid band over a central third of a height (h₄) of said band is at least2% less with respect to a diameter (D₂₂₄) of said band at said points ofattachment of said trailing edges of said blades on said band.
 8. Ahydraulic machine of Francis type equipped with a runner, said runnercomprising: a crown; a band; and blades extending between said crown andsaid band such that a leading edge of each of said blades has points ofattachment with said crown and said band and a trailing edge of each ofsaid blades has other points of attachment with said crown and saidband, said blades defining between themselves channels for flow ofliquid and being rotatable with said crown and said band in a directiondefined by a linear component (U), and each of said blades hasoppositely oriented lateral faces which are spaced equidistant from animaginary curved median line extending from said leading edge to saidtrailing edge; wherein an angle (β₂₄) between the direction defined bythe linear component (U) of each of said blades and a straight line(Δ₂₂₄) extending from the median line of each of said blades at saidtrailing edge thereof, has, at said point of attachment of each of saidblades on said band, a value between 20 and 25°.
 9. The hydraulicmachine according to claim 8, further comprising a turbine delivering anequivalent power under high load (P_(11FC)), which corresponds to apower of said turbine at a working point (B) where the efficiency isless by 3.5% than the efficiency at an optimum working point (A), underone meter of head and with a runner outlet diameter of one meter,expressed in kilowatts, such that a ratio with a speed of rotation (N₁₁)of said turbine under the same conditions, expressed in revolutions perminute, has a value between 0.16 and 0.175.